Question

If - 3 + ${ix}^{2}yand{x}^2+y+4i$ be conjugate of each other, then the value of x and y is

• A.
• B. - 1 , 4
• C.
• D. None of these

Answer 1

The correct option is A

We are given that $\overline{-3+{ix}^{2}y}=x^2+y+4i$ (given)
i.e. - 3 - ${ix}^{2}y=x^2+y+4i$
$-$ 3 = $x^2+yand{x}^{2}y=-4$
The quadratic equation whose roots are $x^2$ and y is
$t^2-(x^2+y)t+x^{2}y$
$t^2+3t-4=0$
t = 4, t = 1
As $x^{23}0,$ we taken $x^2$ = 1 and y = $-$ 4
So, x = $\pm 1$, y = $-$ 4